Show that the squares of the 2n-th roots of unity are the n-th roots of unity. hint: this requires showing two things: (1) the square of every 2n-th root of unity is an n-th root of unity, and (2) every n-th root of unity is the square of some 2n-th root of unity

If gases like carbon dioxide and methane make up less than 1% of the total atmosphere, why is it important for scientists to monitor changes in percentages of these gases?

Apatient has a history of poor nutrition. he has skin rashes, bleeding gums, and a cut that hasn’t healed in a long time. what vitamin deficiency most likely caused this symptom?

In the future, people will only enjoy one sport: electrodisc. in this sport, you gain points when you cause metallic discs hovering on a field to exchange charge. you are an electrodisc player playing the popular four disc variant. the disks have charges of qa = −8.0 µc, qb = −2.0 µc, qc = +5.0 µc, and qd = +12.0 µc. (1) you bring two disks together and then separate them. you measure the resulting charge of these two disks and find that it is +5.0 µc per disk. which two disks did you bring together? (a) a and b (b) a and c (c)a and d (d)b and c(e) b and d (f) c and d. (2) you bring three disks together and then separate them. you measure the resulting charge of these three disks and find that it is +3.0 µc per disk. which three disks did you bring together? a, b, and c (a) a, b, and d (c) a, c, and d (d) b, c, and d. (3) given the resulting charge of each disk measured in (b) is +3.0 µc, how many electrons would you need to add to a disk of this charge to electrically neutralize it? electrons